Smith–Purcell radiation (SPR) is the electromagnetic wave generated by free electrons passing above a diffraction grating, and it has played an important role in free-electron light sources and particle accelerators. Orbital angular momentum (OAM) is a new degree of freedom that can significantly promote the capacity of information carried by an electro-magnetic beam. In this paper, we propose an integrable method for generating vortex Smith–Purcell radiation (VSPR), namely, SPR carrying OAM, by having free-electron bunches pass on planar holographic gratings. VSPRs generated by different electron energies, with different topological charges of the OAM, radiation angles, and frequencies are demonstrated numerically. It is also found that, for high-order radiation, the topological charge of the OAM wave will be multiplied by the radiation order. This work introduces a new way to generate SPR with OAM and provides a method to achieve an integratable and tunable free-electron OAM wave source at different frequency regions.